Messi continued to cut the gap on Cristiano Ronaldo as the Champions League's all-time top goalscorer.
Barca had already booked their place in the last 16 as Group C winners, but were looking for a morale boosting win after three successive draws, including the concession of a last minute equaliser to Real Madrid in a 1-1 draw on Saturday.
Messi continued to cut the gap on Cristiano Ronaldo as the Champions League's all-time top goalscorer when he slotted home the opener after just 16 minutes.
Turan then struck his first Barca hat-trick in a 17-minute second-half spell as the hosts took out their frustration on a dispirited Monchengladbach.
"I have to congratulate the players because today was a game in which we had little to win and things could have gone very differently," Barca boss Luis Enrique told BeIN Sports Spain.
"It is perhaps the most precise we have been all season and it came in a game where we didn't have a lot of space to play in."
Whilst Barca can look forward to the last 16 for a 13th straight season, third place in the group behind Manchester City ensures Moenchengladbach drop into the Europa League.
"We had too much respect for them and didn't play with enough courage," said Moenchengladbach boss Andre Schubert.
Enrique retained only Messi, Andre Gomes and Javier Mascherano from the side that started El Clasico on Saturday.
And Messi's insatiable appetite for goal was rewarded when he exchanged passes with Turan to sweep home his 93rd in the Champions League, now just three adrift of Ronaldo in the race to be the first man to a 100.
The five-time World Player of the Year was the persistent threat throughout the first 45 minutes, but Barca captain Andres Iniesta also impressed on his first start for six weeks after a knee injury.
Only Moenchengladbach 'keeper Yann Sommer prevented Messi from adding to his tally before half-time.
However, it was Turan who took centre stage after the break as he responded to criticism for committing the foul which led to Sergio Ramos's equaliser for Madrid on Saturday.
"One moment doesn't decide a game," said Enrique in defence of the midfielder.
"We are not focused on that and no matter what happens, players always need to score goals."
Turan was perfectly placed to head home Denis Suarez's deflected cross home at the back post before producing a fine low finish into the far corner from Aleix Vidal's cut-back.
Paco Alcacer's search for a first goal since his 30 million euro ($32 million) move from Valencia goes on.
Yet, Alacacer did at least make a contribution as it was from his low cross that Turan completed his hat-trick with a powerful finish at the back post that was too strong for Sommer to keep out.